The pattern can be expressed another way that may be more useful in practice.

So far, we’ve just replaced 7 with x and 8 with x+1. We can instead replace the 8 with y and the -1 with -(x–y)2. We then have

xy = ((x+y)2-(x–y)2)/4.

Expanding the right-hand side then simplifying gives:

xy = ((x2+2xy+y2)-(x2-2xy+y2))/4
= 4xy/4 ,

again confirming the pattern.

This pattern is more useful because it tells us that the product of any two numbers x and y equals one quarter the difference between the square of their sums, and the square of their difference. The example given for 56 is a special case. The product of any two consecutive numbers is one quarter of the difference between the square of their sums, and 1.